Temporally varying 3D computer graphics models find broad application in the classic computer graphics today. 3D computer graphics models, for example, find application in games, virtual worlds, cartoon productions, etc., but also in more recent systems, which are referred to as Free Viewpoint Video (FVV) or 3D Video Objects (3DVO).
3D computer graphics models describe the surface of 3D objects in a virtual 3D coordinate system. To this end, the 3D coordinates (x, y, z) of a certain number of control points or vertices lying on the surface or arranged along the same are defined. The continuous surface is defined by different approaches of the parameterization. In a parameterization referred to as polygon mesh, the shape of the surface of 3D objects, for example, is defined by polygons, the corner points of which form the control points. For the complete description of an object, the indication of connectivity, i.e. the indication as to which control points are each summarized to polygons, also belongs here. The complete 3D object then develops by association of color, texture and further features, such as reflection, etc. Depending on surface parameterization used, these features are associated with the connectivity or directly with the point representation.
The usual representation of a 3D geometry thus is the indication of 3D coordinates of control points in a list with or without indication of their connectivity. In the case of the above-mentioned polygon connectivity for a triangle mesh, for example, three control points each at the corresponding list numbers form a triangle, which are again summarized in a list. The 3D coordinates may be present as floating-point or integer values. The connectivity consists of integer values, namely the indication of list numbers at which the corresponding control points are arranged in the list.
For exchanging and transmitting the 3D geometry between various systems and applications, it is desirable to use a specified text format, such as Virtual Reality Modelling Language (VRML), because this enables parsing the 3D data on the reception side.
Moreover, above all, it is also desirable to reduce the necessary amount of data for coding a 3D geometry, in order to reduce transmission data rate and necessary memory space. Such a reduction can be attained if special compression methods are employed. For this reason, in the MPEG-4 standard, a method for coding the 3D geometry of static objects was standardized, which is referred to as 3D Mesh Coding (3DMC). 3DMC is a binary format, which also makes functionalities for the transmission improved as opposed to the text format available, apart from 30 to 40-fold compression.
In a plurality of applications, however, dynamic, i.e. temporally varying, 3D models occur. In the classic computer graphics, these develop by animation, with an operator often newly establishing the model for each time instant. In more recent methods of FVV or 3DVO, dynamic models develop by the reconstruction of the 3D movement of real objects, which are recorded by several cameras. Basically, it can be discriminated between two cases of dynamic 3D models. In the first case, the topology remains the same, i.e. the number of control points or vertices and the connectivity are constant over time. Only the 3D position of the control points changes. The second case represents a generalization. In this case, changes in the topology are also admissible.
In some cases, the temporal change can be described by animation, i.e. by describing the changes by means of an underlying physical movement model. Examples for this are the animation of human faces and bodies, which are already standardized, also in MPEG-4, namely by the so-called FBA (Face and Body Animation) method. Such animation models are disadvantageous in that they are not transferable to a general case, i.e. that they are restricted to special movement sequences and/or special objects, such as faces, etc. If no animation model exists, for each time instant, rather a new 3D model or a new mesh of control points has to be transferred, which is then coded for each time instant with MPEG-4 3DMC, but since it is the same object in motion at every time instant, this data still contains a lot of temporal redundancy, which could be used for further compression.
In J. Zhang and C. B. Owen, “Octree-based Animated Geometry Compression”, DCC'04, Data Compression Conference, Snowbird, Utah, USA, pages 508-517, Mar. 23-25, 2004, a method of coding temporally varying 3D models is described in which the temporal change is described by prediction of the control points, quantization of the prediction error or the motion vectors and summarizing motion vectors to groups. The compression, i.e. the reduction in the bit rate, is done following the general principle of Differential Pulse Code Modulation (DPCM). In this manner, even more significant compression gains, i.e. bit-rate savings at equal quality or better quality at equal bit-rate, can be attained for dynamic models as opposed to 3DMC.
With the increasing employment of 3D models in the most diverse field of application, however, the need for more effective coding schemes for better compression of dynamic models increases.